Secondly, since the coefficients are independent of \(t\) , \(\partial _tu\)  is also a weak solution of \(L\)  (see Appendix , Remark REF ), and thus \(\partial _tu\)  satisfies Harnack Principle and interior Hölder estimates (see [1]}). This allows us to apply a well-known result for Carleson measures (see, e.g., [2]} Lemma 2.14), to deduce from (REF ) an apparently stronger bound
\(\int _0^{l(Q)}\int _Q\left|\partial _tu(x,t)\right|^2t\,dx\lesssim \left|Q\right|.\) 
